Theorem clmring

Description: The scalar ring of a subcomplex module is a ring. (Contributed by Mario Carneiro, 16-Oct-2015)

	Ref	Expression
Hypothesis	clm0.f	|- F = ( Scalar ` W )
Assertion	clmring	|- ( W e. CMod -> F e. Ring )

Proof

Step	Hyp	Ref	Expression
1		clm0.f	|- F = ( Scalar ` W )
2		clmlmod	|- ( W e. CMod -> W e. LMod )
3	1	lmodring	|- ( W e. LMod -> F e. Ring )
4	2 3	syl	|- ( W e. CMod -> F e. Ring )